DelaunayTriangulationTraits Concept Reference

Definition

This concept describes the geometric types and predicates required to build a Delaunay triangulation. It corresponds to the first template parameter of the class Delaunay_triangulation<DelaunayTriangulationTraits, TriangulationDataStructure>.

Refines:

TriangulationTraits.

Has Models:

CGAL::Cartesian_d<FT, Dim, LA>

CGAL::Epick_d<Dim> (recommended)

See Also

TriangulationTraits

DelaunayTriangulation

Types
typedef unspecified_type	Side_of_oriented_sphere_d
	A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Point_d & p). More...
typedef unspecified_type	In_flat_side_of_oriented_sphere_d
	A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(Flat_orientation_d orient, ForwardIterator start, ForwardIterator end, const Point_d & p). More...

Creation
	DelaunayTriangulationTraits ()
	The default constructor.

Operations
The following methods permit access to the traits class's predicates:
Side_of_oriented_sphere_d	side_of_oriented_sphere_d_object () const
In_flat_side_of_oriented_sphere_d	in_flat_side_of_oriented_sphere_d_object () const

Member Typedef Documentation

typedef unspecified_type DelaunayTriangulationTraits::In_flat_side_of_oriented_sphere_d

A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(Flat_orientation_d orient, ForwardIterator start, ForwardIterator end, const Point_d & p).

The operator returns ON_POSITIVE_SIDE, ON_NEGATIVE_SIDE or ON_ORIENTED_BOUNDARY depending of the side of the query point p with respect to the sphere circumscribing the simplex defined by the points in range [start,end). If the simplex is positively oriented according to orient, then the positive side of sphere corresponds geometrically to its bounded side. The points in range [start,end) and p are supposed to belong to the lower dimensional flat whose orientation is given by orient.

Precondition

std::distance(start,end)=k+1 where \( k\) is the number of points used to construct orient. The points in range [start,end) must be affinely independent, i.e., the simplex must not be flat. p must be in the flat generated by this simplex.

typedef unspecified_type DelaunayTriangulationTraits::Side_of_oriented_sphere_d

A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Point_d & p).

The operator returns ON_POSITIVE_SIDE, ON_NEGATIVE_SIDE or ON_ORIENTED_BOUNDARY depending of the side of the query point p with respect to the sphere circumscribing the simplex defined by the points in range [start,end). If the simplex is positively oriented, then the positive side of sphere corresponds geometrically to its bounded side.

Precondition

If Dimension=CGAL::Dimension_tag<D>, then std::distance(start,end)=D+1. The points in range [start,end) must be affinely independent, i.e., the simplex must not be flat.